National open university of nigeria introduction to econometrics I eco 355

3.2.1 The Assumptions 
The CLRM consists of eight basic assumptions about the ways in which the observations 
are generated: 
1.
Linearity: The first assumption is that the dependent variable can be calculated as 
a linear function of a specific set of independent variables, plus a disturbance term.
This can be expressed mathematically as follows: The regression model is linear 
in the unknown coefficients
so that 
2. 
has some variation: By this assumption we mean that not all observations of 
are the same, at least one has to be different so that the sample 
is not 0. It 
is important to distinguish between the sample variance, which simply shows how 
much X varies over the particular sample, and the stochastic nature of X. in 
course, we shall make the assumption that X is non-stochastic. This means that 
the variance of X at any point in time is zero, so 
is not 0. It is important 
to distinguish between the sample variance, which simply shows how much X 
varies over the particular sampl, and the stochastice nature of X. In course, we 
shall make the assumption that X is non-stochastic. This means that the variance 
of X at any point in time is zero, so
, and if we could somehow repeat 
the world over againX would always take exactly the same values. But of course, 
over any sample there will (indeed must) be some variations in X. 
3. 
is non-stochastic and fixed in repeated samples. By these assumptions we 
mean first that 
is a variable whose value are not determined by some chance 
mechanism, that is they are determined by an experimenter or investigator, and 
seen that it is possible to repeat the sample with the same independent variable 
values. This implies that 
for all s, and t =1, 2 ……., n: that is 
and 
are uncorrelated. 
4. 
The expected value of the disturbance term is zero: - This means that the 
disturbance is a genuine disturbance, so that if we took a large number of samples 
the mean disturbance would be zero. This can be denoted as
. We 
need this assumption in order to interpret the deterministic part of a regression 
model, 
as a statistical average relation. 

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5. 
Homoskedasticity: This requires that all disturbance terms have the same 
variance, so that 
= 
= constant for all t. 
6. 
Serial independence: This requires that all disturbance terms are independently 
distributed, or, more easily, are not correlated with one another, so that 
for 
all 
s. 
This 
assumption has a special significance in economics to grasp what it means in 
practice, recall that we nearly always obtain our data from time series in which 
each t is one year, or one quarter, or one week ahead of the last. The condition 
means, therefore, that the disturbance is one period should not be related to a 
disturbance in the next or previous periods. This condition is frequently violated 
since, if there is a disturbing effect at one time, it is likely to persist. 
7. 
Normality of Residuals: The disturbance 
are assumed to be 
independently and identically normally distributed, with mean zero and common 
variance 
. 
8. 
n>2 and multicollinearity: This assumption says that the number of observations 
must be greater than two or in general than the relationships among the variables.